相关论文: Transport-majorization to analytic and geometric i…

We analyze a class of linear partial differential equations that arise as deterministic descriptions of the scaling limits of L\'evy walks, in which transport is driven by a convex combination of fractional material derivatives and a source…

We develop a theory of optimal transport for stationary random measures with a focus on stationary point processes and construct a family of distances on the set of stationary random measures. These induce a natural notion of interpolation…

The quadratically regularized optimal transport problem is empirically known to have sparse solutions: its optimal coupling $\pi_{\varepsilon}$ has sparse support for small regularization parameter $\varepsilon$, in contrast to entropic…

We compare weighted sums of i.i.d. positive random variables according to the usual stochastic order. The main inequalities are derived using majorization techniques under certain log-concavity assumptions. Specifically, let $Y_i$ be i.i.d.…

This work deals with the asymptotic distribution of both potentials and couplings of entropic regularized optimal transport for compactly supported probabilities in $\R^d$. We first provide the central limit theorem of the Sinkhorn…

We propose to tackle the problem of understanding the effect of regularization in Sinkhorn algotihms. In the case of Gaussian distributions we provide a closed form for the regularized optimal transport which enables to provide a better…

The classical problem of optimal transportation can be formulated as a linear optimization problem on a convex domain: among all joint measures with fixed marginals find the optimal one, where optimality is measured against a cost function.…

We review some simple techniques based on monotone mass transport that allow to obtain transport-type inequalities for any log-concave probability measure, and for more general measures as well. We discuss quantitative forms of these…

We show that if the random walk on a graph has positive coarse Ricci curvature in the sense of Ollivier, then the stationary measure satisfies a W^1 transport-entropy inequality. Peres and Tetali have conjectured a stronger consequence,…

Fix probability densities $f$ and $g$ on open sets $X \subset \mathbf{R}^m$ and $Y \subset \mathbf{R}^n$ with $m\ge n\ge1$. Consider transporting $f$ onto $g$ so as to minimize the cost $-s(x,y)$. We give a non-degeneracy condition (a) on…

We prove a log-Sobolev inequality for a certain class of log-concave measures in high dimension. These are the probability measures supported on the unit cube in R^n whose density takes the form exp(-H) where the function H is assumed to be…

In this paper, we give necessary and sufficient conditions for Talagrand's like transportation cost inequalities on the real line. This brings a new wide class of examples of probability measures enjoying a dimension-free concentration of…

In this paper, we study the connection between entropic optimal transport and entropy power inequality (EPI). First, we prove an HWI-type inequality making use of the infinitesimal displacement convexity of optimal transport map. Second, we…

This note presents a sharp transport-entropy inequality that improves on Talagrand's inequality for the Gaussian measure, arising as a dual formulation of the functional Santal\'o inequality. We also discuss some extensions and connections…

It is well known that martingale transport plans between marginals $\mu\neq\nu$ are never given by Monge maps -- with the understanding that the map is over the first marginal $\mu$, or forward in time. Here, we change the perspective, with…

We prove the existence of generalised solutions of the Monge-Kantorovich equations with fractional $s$-gradient constraint, $0<s<1$, associated to a general, possibly degenerate, linear fractional operator of the type, \begin{equation*}…

We prove upper bounds on the $L^\infty$-Wasserstein distance from optimal transport between strongly log-concave probability densities and log-Lipschitz perturbations. In the simplest setting, such a bound amounts to a transport-information…

We investigate the Brenier map $\nabla \Phi$ between the uniform measures on two convex domains in $\mathbb{R}^n$ or more generally, between two log-concave probability measures on $\mathbb{R}^n$. We show that the eigenvalues of the Hessian…

We prove a geometric linearisation result for minimisers of optimal transport problems where the cost-function is strongly p-convex and of p-growth. Initial and target measures are allowed to be rough, but are assumed to be close to…

We study concentration properties for laws of non-linear Gaussian functionals on metric spaces. Our focus lies on measures with non-Gaussian tail behaviour which are beyond the reach of Talagrand's classical Transportation-Cost Inequalities…